Thermal Expansion

[MiKelPD]

I'm looking for information or equations to use for thermal expansion of a stainless steel bore with an acrylic tube inside. The SS bore is approximately 1" ID. What I am trying to accomplish is to size the acrylic tube accordingly as well as a radial snap fit within the bore. How does radial thermal expansion differ from linear thermal expansion?

Any help would be greatly appreciated.

Thanks
ML

 

[drawoh]

MiKelPD,

I don't see why there should be any difference between radial expansion and linear expansion. Tbey are both linear.

Can you design a snap fit based on a solid part? I didn't know any useful material was that flexible. This is especially a problem given that plastics have much larger thermal expansion coefficients than metals.

If your snap-in structure is a cantilever finger, you can assume much more flexibility. You can design for gross deformation, like a millimeter or two, and ignore the effect of thermal expansion.

JHG

 

[desertfox]

Hi MiKelPD

The coeff of linear expansion and the temperature rise is all you need to calculate the expansion of the ss tube ie:-

expansion=(2 x coeff of linear expansion x rad of tube
x temp rise).

However if your trying to achieve an interference fit between the two tubes for an assembly, then you need to relate the difference in diameter of the mating cylinders to the stresses this will produce. This difference in diameter at the "common" surface is termed shrinkage or interference allowance.
Once you have decided on an interference value you can proceed to calculate the pressure between the two cylinders using the following formula:-


p= (X/(2*Rb))* ((Ei*Eo)/[(Eo(K3-Vi)+Ei(K2+Vo)])


where p= radial pressure between cylinders
Rb= outer radius of inner cylinder
Ei,Eo=modulus of elasticity for inner and outer
cylinders
Vi,Vo=Poisson's ratio of inner and outer cylinders

K2=((Rc/Rb)^2 + 1)/((Rc/Rb)^2 - 1)
K3=((Rb/Ra)^2 + 1)/((Rb/Ra)^2 - 1)
K1= 1/[(Rc/Rb)^2 - 1]
K4= 1/[(Rb/Ra)^2 - 1]

where Ra= inner radius of inner cylinder (0 for a solid
shaft)
Rc= outer radius of outer cylinder

and thus stresses in the compound assembly are:-

inner cylinder:-

stress= -p*K4 at Ra
stress= -p*K3 at Rb


outer cylinder:-

stress= -p*K2 at Rb
stress= -p*K1 at Rc

hope this helps

 

[poetix99]

It is not likely to be a major consideration in your particular case, with what I take to be thin walled tubing, but it is worth noting in general that the assumption of uniform radial thermal expansion requires uniform heating - radial and circumferential; otherwise thermal stresses will be induced.